Measurement of h/e Using the Photoelectric Effect and a Mercury Light SourceH. Potter, and E. Kager(Completed 3 December 2005)The ratio of Planck’s constant to the elementary charge was determined to be 3.89x10-15 ± 0.33x10-15 J-s/C with 95% confidence, an interval that includes the currently accepted value1 of 4.14x10-15 J-s/C.I. IntroductionThe quantization of subatomic physics was established in the early 20th Century through the work of numerous physicists. One such physicist was the young Albert Einstein, whose 1905 paper on the photoelectric effect and its relation to the quantization of light lent credence to the hypothesis that light could be best characterized as a particle under certain circumstances. The photoelectric effect also opened a new avenue that could be used to measure Planck’s constant.II. ExperimentA mercury light source was placed opposite a phototube with a lens and a filter. This phototube was connected to a picoampere amplifier, a device that measures current. The incoming light from the mercury light source entered the phototube and created a small current flow in the picoampere amplifier due to the photoelectric effect. In order tocontrol the magnitude of this flow the freed electrons were made to flow against an adjustable voltage. By slowly increasing the opposing voltage, the current was made to decrease until it was as close to zero as experimentally possible. This V0, at which no current flowed, was recorded for 5 specific wavelengths of light emitted by the mercury source. Each specific wavelength was isolated by placing a specific interference filter over the mercury source. According to quantum theory regarding the photoelectric effect,this stopping voltage should be given byewfehV00, (1)where h is Planck’s constant, e is the elementary charge, w0 is a minimal work function that is a characteristic specific to the substance from which electrons are being freed, and f is the frequency of the incoming light. By plotting the 5 points in the form (f,V0) and finding the slope of the corresponding least squares regression line, the ratio h/e was calculated experimentally. In order to determine each stopping voltage more accurately, an additional voltmeter with a digital display that was sensitive in the microvolt range was connected in parallel to the picoampere amplifier, which had an analog display that was poorly suited to determining exactly when zero current was achieved.III. Results and Data AnalysisTable1: All constants used in calculating expected values and frequency data fromobserved wavelengths1, as well as all experimental data and parameters for the linear regression performed on f and V0.Figure 1: A plot of the data alongside its corresponding best-fit line determined through least squares regression analysis.The value of h/e was determined to be 3.89x10-15 ± .33x10-15 J-s/C with 95% confidence. The value of h/e, based upon the data, was taken to be the slope of the least squares regression line, which is provided above in Figure 1. The width of the 95% confidence interval was found by multiplying the standard error in the slope, found using a statistical analysis package, by the two-sided 95% confidence t-value for 3 degrees of freedom, as calculated by a TI-83 graphing calculator. This is an appropriate procedure for determining a confidence interval for a slope that was determined experimentally. The standard error in the slope serves as a standard deviation for the slope value, and by multiplying by the desired t-value a confidence interval of the desired level of 2significance can be made. The number of degrees of freedom used when determining thet-value is 2 fewer than the number of data points plotted.IV. ConclusionSince the currently accepted value1 for h/e, 4.14x10-15 J-s/C, lies within the 95% confidence interval for h/e, 3.89x10-15 ± .33x10-15 J-s/C, the experimental value was within the expected margins of error from the currently accepted value.1Tipler, Paul A. and Ralph A. Llewellyn, Modern Physics, 3rd ed. (W. H. Freeman and Company, New York